1/3x+4+12x-5=8/3x+1

Solution for 1/3x+4+12x-5=8/3x+1 equation:

1/3x+4+12x-5=8/3x+1

We move all terms to the left:

1/3x+4+12x-5-(8/3x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We add all the numbers together, and all the variables

12x+1/3x-(8/3x+1)-1=0

We get rid of parentheses

12x+1/3x-8/3x-1-1=0

We multiply all the terms by the denominator


12x*3x-1*3x-1*3x+1-8=0

We add all the numbers together, and all the variables

12x*3x-1*3x-1*3x-7=0

Wy multiply elements

36x^2-3x-3x-7=0

We add all the numbers together, and all the variables

36x^2-6x-7=0

a = 36; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·36·(-7)
Δ = 1044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{29}}{2*36}=\frac{6-6\sqrt{29}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{29}}{2*36}=\frac{6+6\sqrt{29}}{72}
$